Spherical Designs via Brouwer Fixed Point Theorem

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jan 2010Embargo end date: 01 Jan 2008 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Discrete Mathematics, volume 24, pages 207-217 (issn: 0895-4801, eissn: 1095-7146,

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Authors: Andriy V. Bondarenko; Maryna S. Viazovska;

doi: 10.1137/080738313 , 10.48550/arxiv.0811.1416

arXiv: 0811.1416

handle: 21.11116/0000-0004-2361-7 , 21.11116/0000-0004-2363-5

Spherical Designs via Brouwer Fixed Point Theorem

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Abstract

For each N>=c_d*n^{2d*(d+1)/(d+2)} we prove the existence of a spherical n-design on S^d consisting of N points, where c_d is a constant depending only on $d$.

17 pages

Keywords

FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA)

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